Based on what you've described, it doesn't appear you have any meritorious grounds to bring any claim against the university police.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-668-3790 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at don@HawbakerLaw.) An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated my Law Office as a debt relief agency that can help people file bankruptcy.
Yes, you can sue - anyone can sue anybody. But you'll have to consider whether you want to pay someone to help you do all of this. If you do it on your own you'll get nowhere, so you'll have to pay an attorney. I suggest you let this one go because it will cost you more in the long run that you could hope to obtain.
I'll add to the other responses and point out one thing is missing - your involvement with the incident or the person who had the gun. You were careful to dance around that issue by telling us that there is "no evidence" and that no one could say you were there (although you start off by telling us you were there). Even if you had a valid case for a lawsuit, it would be based on the whole story - not just the parts you chose to tell us.
I disagree (respectfully) with the responses you have received. The circumstances you have described may give rise to a civil rights claim for false arrest under federal law and/or state law, depending on wether you were attending a private university or a public one. The standard for swearing out an arrest warrant is probable cause. LEO had access to your criminal history, so they should have known whether you were convicted of a felony. It is a separate crime to carry a weapon on school grounds, so your ability to file a lawsuit would tern on the evidence supporting the fact that the gun was yours. Most civil rights attorneys will take a case like this (if it has merit) on a contingency fee basis. We have filed and had success in cases of false arrest against UGA police and Clark Atlanta University. Feel free to call our office for a consultation.
This response is provided for informational purposes only. It is not a consultation and is not legal advice. You should not act or fail to act in reliance upon the information provided in this response. This communication does not establish an attorney-client relationship between you and our Firm. You should always consult with an attorney prior to taking any action with regard to a potential legal problem.